Group #21448044 — subgroups

Subgroups — #21448044

Order 7808.

160 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840139	C₂	1	1	yes	maximal, characteristic
2	#16839562	C₂	1	4	yes	maximal, complemented
3	C₄×#11758185	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#500	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₄₈₈	—	2	1	no	—
6	C₂×D₄₈₈	C₂²	1	2	yes	—
7	#14519774	—	2	1	no	—
8	C₂×#11758185	C₂²	1	2	yes	—
9	C₄⋊Q₈×C₆₁	—	2	1	no	—
10	#107×C₆₁	—	2	1	no	—
11	#107×C₆₁	C₂²	1	2	yes	—
12	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
13	C₂×Q₈×C₆₁	—	4	1	no	—
14	C₂×D₂₄₄	—	2	2	no	—
15	C₂×D₂₄₄	—	4	1	no	—
16	C₂×D₂₄₄	—	4	1	no	—
17	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
18	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
19	C₄⋊C₄×C₆₁	—	2	2	no	—
20	C₄⋊C₄×C₆₁	—	4	1	no	—
21	C₄²×C₆₁	D₄	1	1	yes	characteristic
22	D₄₈₈	—	2	4	no	—
23	D₄₈₈	—	4	2	no	—
24	#11758185	—	2	2	no	—
25	C₂²×D₆₁	—	4	2	no	—
26	Q₈×C₆₁	—	8	2	no	—
27	C₂×C₄×C₆₁	—	4	2	no	—
28	C₂×C₄×C₆₁	D₈	1	1	yes	characteristic
29	C₂×C₄×C₆₁	D₈	1	1	yes	characteristic
30	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
31	D₂₄₄	—	4	2	no	—
32	D₂₄₄	—	4	2	no	—
33	D₂₄₄	—	8	2	no	—
34	D₂₄₄	—	8	2	no	—
35	C₈×C₆₁	SD₁₆	1	2	yes	—
36	C₈×C₆₁	#41	1	2	yes	—
37	C₂²×C₆₁	C₂×D₈	1	1	yes	characteristic
38	C₂×D₆₁	—	8	2	no	—
39	C₂×D₆₁	—	8	2	no	—
40	C₂×D₆₁	—	8	2	no	—
41	C₄×C₆₁	—	8	2	no	—
42	C₄×C₆₁	D₁₆	1	2	yes	—
43	C₄×C₆₁	SD₃₂	1	2	yes	—
44	C₄×C₆₁	#124	1	1	yes	characteristic
45	C₄×C₆₁	C₂×SD₁₆	1	1	yes	characteristic
46	#2240	—	61	1	no	maximal, Sylow
47	C₂×C₆₁	#486	1	1	yes	characteristic
48	C₂×C₆₁	C₂×D₁₆	1	1	yes	characteristic
49	C₂×C₆₁	C₂×SD₃₂	1	1	yes	characteristic
50	D₆₁	—	16	2	no	—
51	#500	D₆₁	1	1	yes	characteristic, complemented
52	#493	—	61	1	no	—
53	#357	—	61	4	no	—
54	C₄×C₁₆	—	61	1	no	—
55	C₆₁	#2240	1	1	yes	characteristic, complemented, Sylow
56	C₂×D₈	—	61	2	no	—
57	C₂×D₈	—	122	1	no	—
58	C₄⋊Q₈	—	2	1	no	—
59	#127	—	122	1	no	—
60	C₂×C₁₆	—	61	2	no	—
61	#107	—	2	1	no	—
62	#107	C₂×D₆₁	1	2	yes	—
63	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
64	C₂×Q₈	—	4	1	no	—
65	C₂×D₄	—	122	2	no	—
66	C₂×D₄	—	244	1	no	—
67	C₂×D₄	—	244	1	no	—
68	D₈	—	122	4	no	—
69	D₈	—	244	2	no	—
70	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
71	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
72	C₄⋊C₄	—	2	2	no	—
73	C₄⋊C₄	—	4	1	no	—
74	C₄²	C₂²⋊D₆₁	1	1	yes	characteristic
75	C₁₆	—	122	2	no	—
76	C₂³	—	244	2	no	—
77	Q₈	—	8	2	no	—
78	D₄	—	488	2	no	—
79	D₄	—	488	2	no	—
80	D₄	—	244	2	no	—
81	D₄	—	244	2	no	—
82	C₂×C₄	—	4	2	no	—
83	C₂×C₄	#11758199	1	1	yes	characteristic
84	C₂×C₄	#11758199	1	1	yes	characteristic
85	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
86	C₈	#11758201	1	2	yes	—
87	C₈	#11758226	1	2	yes	—
88	C₂²	—	488	2	no	—
89	C₂²	—	488	2	no	—
90	C₂²	—	488	2	no	—
91	C₂²	C₂×#11758199	1	1	yes	characteristic
92	C₄	—	8	2	no	—
93	C₄	#14519718	1	2	yes	—
94	C₄	#14519720	1	2	yes	—
95	C₄	#14519766	1	1	yes	characteristic
96	C₄	C₂×#11758201	1	1	yes	characteristic
97	C₂	—	976	2	no	—
98	C₂	#16840110	1	1	yes	characteristic
99	C₂	C₂×#14519718	1	1	yes	characteristic
100	C₂	C₂×#14519720	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840139

C₂

yes

maximal, characteristic

#16839562

C₂

yes

maximal, complemented

C₄×#11758185

C₂

yes

maximal, characteristic, complemented

C₆₁×#500

C₂

yes

maximal, characteristic, complemented

C₂×D₄₈₈

—

C₂×D₄₈₈

C₂²

yes

—

#14519774

—

C₂×#11758185

C₂²

yes

—

C₄⋊Q₈×C₆₁

—

#107×C₆₁

—

#107×C₆₁

C₂²

yes

—

C₄×C₈×C₆₁

C₂²

yes

characteristic

C₂×Q₈×C₆₁

—

C₂×D₂₄₄

—

C₂×D₂₄₄

—

C₂×D₂₄₄

—

C₂×C₈×C₆₁

D₄

yes

characteristic

C₂×C₈×C₆₁

C₂³

yes

characteristic

C₄⋊C₄×C₆₁

—

C₄⋊C₄×C₆₁

—

C₄²×C₆₁

D₄

yes

characteristic

D₄₈₈

—

D₄₈₈

—

#11758185

—

C₂²×D₆₁

—

Q₈×C₆₁

—

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

D₈

yes

characteristic

C₂×C₄×C₆₁

D₈

yes

characteristic

C₂×C₄×C₆₁

C₂×D₄

yes

characteristic

D₂₄₄

—

D₂₄₄

—

D₂₄₄

—

D₂₄₄

—

C₈×C₆₁

SD₁₆

yes

—

C₈×C₆₁

#41

yes

—

C₂²×C₆₁

C₂×D₈

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

—

C₄×C₆₁

—

C₄×C₆₁

D₁₆

yes

—

C₄×C₆₁

SD₃₂

yes

—

C₄×C₆₁

#124

yes

characteristic

C₄×C₆₁

C₂×SD₁₆

yes

—

C₂×C₆₁

yes

C₂×C₆₁

C₂×D₁₆

yes

characteristic

C₂×C₆₁

C₂×SD₃₂

yes

characteristic

D₆₁

—

#500

D₆₁

yes

characteristic, complemented

#493

—

#357

—

C₄×C₁₆

—

C₆₁

#2240

yes

characteristic, complemented, Sylow

C₂×D₈

—

C₂×D₈

—

122

—

C₄⋊Q₈

—

#127

—

122

—

C₂×C₁₆

—

#107

—

#107

C₂×D₆₁

yes

—

C₄×C₈

C₂×D₆₁

yes

characteristic

C₂×Q₈

—

C₂×D₄

—

122

—

C₂×D₄

—

244

—

C₂×D₄

—

244

—

D₈

—

122

—

D₈

—

244

—

C₂×C₈

C₂²⋊D₆₁

yes

characteristic

C₂×C₈

C₂²×D₆₁

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₂²⋊D₆₁

yes

characteristic

C₁₆

—

122

—

C₂³

—

244

—

Q₈

—

D₄

—

488

—

D₄

—

488

—

D₄

—

244

—

D₄

—

244

—

C₂×C₄

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂×C₂²⋊D₆₁

yes

characteristic

C₈

#11758201

yes

—

C₈

#11758226

yes

—

C₂²

—

488

—

C₂²

—

488

—

C₂²

—

488

—

C₂²

C₂×#11758199

yes

characteristic

C₄

—

C₄

#14519718

yes

—

C₄

#14519720

yes

—

C₄

yes

C₄

yes

C₂

—

976

—

C₂

yes

C₂

yes

100

C₂

C₂×#14519720

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×#11758199
commutator	C₂×C₈×C₆₁	C₂³
Frattini	C₂×C₈	C₂²×D₆₁
Fitting	C₆₁×#500	C₂
socle	C₂²×C₆₁	C₂×D₈
hypercenter	#500	D₆₁
hypocenter	C₆₁	#2240
LCS	G ▷ C₂×C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #500

subgroup

G/H

center

C₂²

C₂×#11758199

commutator

C₂×C₈×C₆₁

C₂³

Frattini

C₂×C₈

C₂²×D₆₁

Fitting

C₆₁×#500

C₂

socle

C₂²×C₆₁

C₂×D₈

D₆₁

C₆₁

G ▷ C₂×C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #500

N	H ≅ G/N	type
2. #16839562	C₂	semidirect
3. C₄×#11758185	C₂	semidirect
4. C₆₁×#500	C₂	semidirect
51. #500	D₆₁	semidirect
55. C₆₁	#2240	semidirect

H ≅ G/N

type

2. #16839562

C₂

semidirect

3. C₄×#11758185

C₂

semidirect

4. C₆₁×#500

C₂

semidirect

51. #500

D₆₁

semidirect

55. C₆₁

#2240

semidirect

Subgroups — #21448044

Conjugacy classes of subgroups

Complements